A car travels at a speed of 30m/s when it leaves a ramp set at an angle fo 37 degrees from the ground. How high off the ground will the car reach? What is the maximum height of the gorge could the car clear?

Answer:

Explanation:

The decay of a radioactive substance is governed by the formula:N(t) = N₀ e^(-λt)where N₀ is the initial amount of the substance, N(t) is the amount remaining after time t, and λ is the decay constant.The half-life of Iodine-131 is 8 days, which means that after each 8-day period, the amount remaining will be reduced by half. We can use this fact to calculate the amount remaining after 56 days.First, we need to find the decay constant λ, which is related to the half-life by the formula:λ = ln(2) / t½where ln(2) is the natural logarithm of 2, and t½ is the half-life.Substituting the values we have:λ = ln(2) / 8 days ≈ 0.08664 day^(-1)Next, we can use the formula for N(t) to calculate the amount remaining after 56 days:N(56) = N₀ e^(-λt) = 256 g e^(-0.08664 day^(-1) × 56 days) ≈ 22.6 gTherefore, approximately 22.6 grams of the original 256 gram sample would remain after 56 days.

Therefore, Lucy spent 1.875 hours on the remaining 45 questions.

Let's start by finding the total number of questions in Lucy's homework. If she finished 1/4 of her homework at an average speed of 15 questions per hour, then the total number of questions must be:

1/4 x Total number of questions = Number of questions finished at 15 questions per hour

1/4 x Total number of questions = 15 questions per hour

Solving for the total number of questions, we get:

Total number of questions = 60 questions

Now we know that Lucy finished 60 - 45 = 15 questions at an average speed of x questions per hour. Let's use the formula:

time = distance / speed

to find the amount of time she spent on the remaining 45 questions.

For the first part of the homework, Lucy spent:

time = distance / speed

time = 15 questions / hour

time = 1/4 x 2.5 hours

time = 0.625 hours

So, she spent 0.625 hours on the first 15 questions.

For the remaining 45 questions, we have:

time = distance / speed

time = 45 questions / x questions per hour

We know that the total time spent on the homework was 2.5 hours, so:

0.625 hours + 45 questions / x questions per hour = 2.5 hours

Solving for x, we get:

x = 18 questions per hour

Now we can use this speed to find the time spent on the remaining 45 questions:

time = distance / speed

time = 45 questions / 18 questions per hour

time = 2.5 hours - 0.625 hours

time = 1.875 hours

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If a displacement vector is 23 km in length and directed 65° south of east. the components of this vector is: (a) 21 km 9.7 km.

The displacement vector can be resolved into its eastward and southward components using trigonometry. Let's call the eastward component "x" and the southward component "y".

From the given information, we know that the displacement vector makes an angle of 65° south of east. This means that the angle between the vector and the eastward axis is 90° - 65° = 25°.

Using trigonometry, we can relate the length of the vector to its components:

cos 25° = x / 23

sin 25° = y / 23

Solving for x and y, we get:

x = 23 cos 25° ≈ 21 km

y = 23 sin 25° ≈ 9.7 km

Therefore, the answer is (a) 21 km eastward component and 9.7 km southward component.

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Answer: 4 m/s

Explanation:

To solve this problem, we can use the principle of conservation of momentum, which states that the total momentum of a closed system remains constant before and after a collision.

Let's denote the initial velocity of the 2 kg ball as "v1i", the initial velocity of the 6 kg ball as "v2i", the final velocity of the 2 kg ball as "v1f", and the final velocity of the 6 kg ball as "v2f".

According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Mathematically, this can be expressed as:

m1 * v1i + m2 * v2i = m1 * v1f + m2 * v2f

where m1 is the mass of the 2 kg ball, m2 is the mass of the 6 kg ball, v1i and v2i are the initial velocities, and v1f and v2f are the final velocities.

Given:

m1 = 2 kg

m2 = 6 kg

v1i = 12 m/s (initial velocity of the 2 kg ball)

v2i = 0 m/s (initial velocity of the 6 kg ball, as it is stationary)

v1f = 0 m/s (final velocity of the 2 kg ball, as it comes to rest)

Plugging in the given values into the conservation of momentum equation:

2 * 12 + 6 * 0 = 2 * 0 + 6 * v2f

24 = 6 * v2f

Dividing both sides by 6:

v2f = 24 / 6 = 4 m/s

So, the velocity of the 6 kg ball after the collision is 4 m/s.

Supermassive black holes that are devouring gas at the center of far-off galaxies are known as quasars.

Since, the quasars were initially identified by astronomers in 1963 as objects that resembled stars but gave off radio waves instead, the term quasar is an abbreviation for quasi-stellar radio source.

Quasars are so bright that they drown out the light from all other stars in the same galaxy. Quasars give off radio waves, X-rays, gamma-rays, ultraviolet rays, and visible light across the entire electromagnetic spectrum. Most of them are larger than our solar system.

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The speed of sound in Gold Harbour, on a day when the air temperature is -2.7 °C, is 331.5 + 0.6 * (-2.7) = 328.65 m/s.

Gold Harbour is a small settlement located on Antarctic's King George Island. It is home to a Chilean research base, which is operated by the Chilean Antarctic Institute. It also acts as a summer base for the Chilean Navy, and provides support for the scientific research conducted by other countries, including the United States, United Kingdom, and Russia. The area is known for its stunning natural beauty, with mountains, glaciers, and icebergs all in close proximity. It is also an important habitat for several species of wildlife, including penguins, seals, and sea birds.

The speed of sound in air is affected by temperature, and the formula for calculating the speed of sound in air is v = 331.5 + 0.6 * (air temperature in °C).
Therefore, the speed of sound in Gold Harbour, on a day when the air temperature is -2.7 °C, is 331.5 + 0.6 * (-2.7)
= 328.65 m/s.

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The maximum speed of the cart if the amplitude of the motion is 3.00 cm is  0.036 m/s

The velocity of the cart when the position is 2.00 cm is 0.1414 m/s.

The kinetic and potential energies of the system when the position of the cart is 2.00 cm​ is 5×10⁻³ J and 4×10⁻³ J resp.

a) To find maximum speed potential energy of the spring gets converted into kinetic energy of the cart in the oscillator motion, Hence,

1/2mv² =1/2kA²

1/2×0.5×v² = 1/2 ×20× 0.03²

v² = 40×9×10⁻⁴

v = 0.036 m/s

b) For the velocity at a given point is calculated by the formula,

v = ±ω√(A² - x²)

v = ±ω√(0.03² - 0.02²)

v = ±ω × 0.0223

v = ±√k/m × 0.0223

v = ±√20/0.5× 0.0223

v = 0.1414 m/s

c)

kinetic energy of the system,

K = 1/2 mv²

K = 1/2 ×0.5×0.1414²

K = 5×10⁻³ J

Potential energy of the system

P = 1/2 kx²

P = 1/2 × 20× 0.02²

P = 4×10⁻³ J

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The force of attraction between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.

A square is a two-dimensional geometric shape that has four sides of equal length and four right angles (90-degree angles) between them. The sides of a square are parallel to each other and perpendicular to its adjacent sides. All four corners of a square are also known as vertices, and the diagonals of a square bisect each other at right angles.

The area of a square is calculated by multiplying the length of one of its sides by itself. The perimeter of a square is calculated by adding up the lengths of all four sides. The properties of a square make it useful in various applications, such as in geometry, architecture, and construction.

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The given statement, "An overtone is louder than the fundamental tone" is False.

An overtone is a higher-frequency vibration that occurs simultaneously with the fundamental frequency of a sound wave. These vibrations are multiples of the fundamental frequency and contribute to the overall timbre or tone quality of a sound.

In some cases, overtones can be louder than the fundamental tone, depending on the specific harmonic series present in the sound wave. This phenomenon is known as overtone prominence, and it can be heard in certain musical instruments like bells or cymbals, where the higher harmonics of the sound are emphasized.

However, in most cases, the fundamental tone is perceived as the strongest and most dominant sound in a given sound wave.

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Answer:

As a protostar contract, the temperature rises. This increase in temperature leads to the initiation of nuclear fusion reactions, where hydrogen atoms fuse together to form helium, releasing energy in the process. This energy causes the protostar to heat up and begin to emit light, eventually becoming a stable star.

The answer is B. The temperature rises.

Explanation:

Find the time it takes to hit the  bottom....then multiply this time by the horizontal velocity .......

Time to hit bottom :

       d = 1/2 at^2

        9 m  = 1/2 (9.81 m/s^2) (t^2)    shows  t = 1.35 s

Now the horizontal displacement is

      x = rate * time = 24.40 m/s * 1.35 s = 33.1 m

To drive the barrel over the step, the least horizontal force F necessary is 2366.16 N.

To push the barrel over the step, the minimum force required should overcome the force of gravity acting on the barrel and the force of static friction between the barrel and the surface.

The perpendicular component of the weight is given as N = mgcosθ, where m = mass of the barrel,

g = acceleration due to gravity, and

θ = angle between the weight and normal to the surface.

In this case, θ as the inverse tangent of the ratio of the height of step to the distance from the edge of the step to the center of the barrel:

θ = tan⁻¹(0.2/0.5) = 0.39 radians

Therefore, the normal force is N = (1500)(9.81)cos(0.39) = 1443.6 N.

The force of static friction can be found as f = μsN,

where μs = coefficient of static friction.

Assume the coefficient of static friction between the barrel and the surface is 0.6.

f = (0.6)(1443.6) = 866.16 N.

The minimum force required to push the barrel over the step should overcome both these forces. Then, the smallest horizontal force that can push the barrel over the step is:

F = force of gravity + force of static friction

F = 1500 + 866.16

F = 2366.16 N.

Therefore, the smallest horizontal force F required to push the barrel over the step is 2366.16 N.

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When a negatively charged conductive rod is brought close to a lightweight Styrofoam ball suspended from the ceiling by insulating threads (see Figure A), the electrons in the ball are repelled by the rod's negative charge.

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Answer:

9.922

Explanation:

When ignoring the air resistance and the ball is kicked and fell into the same plane. the initial speed is the speed when it is stricken on the ground. the initial momentum magnitude equals the final momentum magnitude only the direction is changed.

∴ Momentum=  mass*velocity  

                      = o.41kg*24.2

                      = 9.922[tex]kgms^{-1[/tex]

You divide by 1000 so it would be 6.785g

The speed of the pendulum at the instant it reaches an angle of 20.6 degrees above the vertical is 3.02 m/s.

A pendulum is a weight suspended from a fixed point that swings back and forth due to the force of gravity.

Based on the given information, we have a pendulum of length 1.06 m and it is released from rest at an angle of 41.2 degrees to the vertical. We need to find the speed of the pendulum at the instant it reaches an angle of 20.6 degrees above the vertical.

To solve this problem, we can use the conservation of mechanical energy. At the highest point of the pendulum's swing, all of its energy is in the form of potential energy, and at the lowest point of its swing, all of its energy is in the form of kinetic energy. Therefore, we can write:

PE_max = KE_min

where PE_max is the potential energy at the maximum height and KE_min is the kinetic energy at the lowest point.

The potential energy of a pendulum is given by:

PE = mgh

where m is the mass of the pendulum, g is the acceleration due to gravity, and h is the height above some reference point.

The kinetic energy of a pendulum is given by:

KE = (1/2)mv^2

where v is the speed of the pendulum.

First, we need to find the vertical height difference between the pendulum's highest and lowest points. To do this, we can use trigonometry:

h = L(1 - cosθ)

where L is the length of the pendulum and θ is the initial angle to the vertical. Substituting the given values, we get:

h = 1.06(1 - cos(41.2°)) = 0.654 m

Next, we can use the conservation of mechanical energy to find the speed of the pendulum at the lowest point of its swing. At this point, all of the potential energy has been converted into kinetic energy, so we can write:

PE_max = KE_min

mgh = (1/2)mv^2

Canceling out the mass, we get:

gh = (1/2)v^2

Solving for v, we get:

v = sqrt(2gh)

where g is the acceleration due to gravity. Substituting the given values, we get:

v = sqrt(2(9.81 m/s^2)(0.654 m)) = 3.78 m/s

Finally, we need to find the speed of the pendulum when it reaches an angle of 20.6 degrees above the vertical. At this point, the pendulum has a potential energy of:

PE = mgh' = mgh cos(20.6°)

where h' is the height of the pendulum at this point. To find h', we can use trigonometry:

h' = L(1 - cosθ')

where θ' is the angle above the vertical. Substituting the given values, we get:

h' = 1.06(1 - cos(20.6°)) = 0.242 m

Substituting the values for h' and solving for the kinetic energy, we get:

KE = PE_max - mgh' = mgh - mgh'

Substituting the known values, we get:

KE = (1 kg)(9.81 m/s^2)(0.654 m) - (1 kg)(9.81 m/s^2)(0.242 m) = 5.11 J

Now, we can solve for the speed at this point:

KE = (1/2)mv^2

5.11 J = (1/2)(1 kg)v^2

v = sqrt((2)(5.11 J)/(1 kg)) = 3.02 m/s

Therefore, The pendulum is moving at a speed of 3.02 m/s when it reaches an angle of 20.6 degrees above vertical.

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Okay, let's convert all the lengths to the same unit to compare:

(a) 100 m = 100 meters

(b) 104 μm = 104 micrometers = 104 × 10^-6 meters = 0.000104 meters

(c) 107 nm = 107 nanometers = 107 × 10^-9 meters = 0.000000000997 meters

(d) 102 mm = 102 millimeters = 102 × 10^-3 meters = 0.0102 meters

The longest length is:

(a) 100 m = 100 meters

The answer is option (a).

Answer: 100 m

Explanation:

1 μm = [tex]10^{-6}[/tex] m = 0,000001 m

1 nm = [tex]10^{-9}[/tex] m = 0,000000001 m

1 mm = [tex]10^{-3}[/tex] m = 0,001 m

∴ 100 m es la mayor longitud

Answer:

A

Opposite poles will attract

This is based on the principle of conservation of energy and momentum.

When the collision of golf balls takes place the energy gets transferred from one ball to the other.

The golf balls experience a force that causes them to change their form and also direction. During the collision, the mechanical energy is converted into heat, sound, and other forms of energy. The rest of energy is used to move in a new direction.

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Answer:

The final velocity is 30 m/s

Explanation:

Use the formula:

[tex]V_{f} = V_{i} +a*t\\V_{f} = 0 + 0.5*60\\V_{f} = 30 m/s[/tex]

Answer:

When a massive star, much larger than our sun, reaches the end of its life cycle, it will undergo a series of fusion reactions in its core until it forms iron, which cannot undergo further fusion. Without fusion to counteract the force of gravity, the core collapses in on itself, causing the outer layers of the star to rapidly expand and creating a red supergiant. Eventually, the outer layers of the star will be expelled in a supernova explosion, leaving behind either a neutron star or a black hole, depending on the mass of the original star. So, the correct answer is B.

Answer:

July 29, Earth completed a full spin in about 1.59 milliseconds shorter than its standard timeframe ( 23 hours and 56 minutes).

The merry-go-round's new angular velocity is 0.321 rpm.

Calculation-

L = Iω

The moment of inertia of a solid disk rotating about its centre is given by:

[tex]I = (1/2)mr^2I = (1/2)(150 kg)(1.5 m)^2 = 168.75 kg·m^2[/tex]

initial angular momentum of the system

L = Iω = [tex](168.75 kg·m^2)(15 rpm)(2π/60 s) = 52.36 kg·m^2/s[/tex]

The new angular velocity is determined by:

L = I'ω'

where L represents the system's initial angular momentum.

The system's new moment of inertia is:

[tex]I' = I - 2mr^2[/tex]

we get:

[tex]I' = 25 kg - 2(168.75 kg/m2)(0.35 m)^2 = 162.88 kg·m^2[/tex]

We get the following by substituting into the conservation of angular momentum equation:

L = I'ω'

[tex](162.88 kg/m2) / 52.36 kg/m2[/tex]

ω' = 0.321 rpm

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Answer:

Here is your answer please change up some words to remain plagraism free.

Explanation:

To determine the required lengths of strings 1 and 2 so that pulses sent in both directions reach the ends of the strings simultaneously, we need to apply the principle that the time it takes for a wave pulse to travel a distance on a string is equal to the distance divided by the wave speed.

The wave speed, in turn, is determined by the tension in the string and the linear density of the string according to the formula:

v = sqrt(T/μ),

where v is the wave speed, T is the tension, and μ is the linear density.

Let L1 be the length of string 1 and L2 be the length of string 2. Since the wave speed is the same for both strings, we can set up the following equations:

L1/v = L2/v

sqrt(T1/μ1)*L1 = sqrt(T2/μ2)*L2

where T1 and T2 are the tensions in strings 1 and 2, respectively.

We can solve for L1 and L2 by combining these two equations and solving for each variable. Substituting the given linear densities of strings 1 and 2, we get:

sqrt(T1/2.60)*L1 = sqrt(T2/3.30)*L2

Squaring both sides and simplifying, we get:

(T1/T2) = (3.30/2.60) * (L1/L2)^2

Substituting the condition that the pulses reach the ends of the strings simultaneously, we know that the total time for a pulse to travel down string 1 and back up to the knot is equal to the time for a pulse to travel down string 2 and back up to the knot. This condition implies that the total length of string 1 (2L1) is equal to the total length of string 2 (2L2):

2L1 = 2L2

Solving this equation for L2 and substituting it into the expression for T1/T2 derived above, we get:

T1/T2 = (3.30/2.60) * (L1/2L1)^2 = 1.25

Solving for L1, we obtain:

L1 = sqrt(T1/μ1) * (2L2/v) = sqrt((1.25)*(2.60/3.30)) * (2L2)

Simplifying this expression, we get:

L1 = (2/3) * sqrt(2.60/3.30) * L2

Therefore, the required length of string 1 is (2/3) * sqrt(2.60/3.30) times the length of string 2. We can substitute the given length of string 2, say L2 = 1 meter, into this expression to obtain the required length of string 1:

L1 = (2/3) * sqrt(2.60/3.30) * 1 meter ≈ 0.693 meter.

Therefore, the required length of string 1 is approximately 0.693 meter and the required length of string 2 is 1 meter.

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Answer:

D

Explanation:

The maximum height reached by a stone thrown straight up with an initial speed of 35 m/s can be found using the kinematic equation:

v^2f = v^2i - 2gh

where vf is the final velocity (0 m/s at the maximum height), vi is the initial velocity (35 m/s, the magnitude of the velocity with which the stone is thrown upwards), g is the acceleration due to gravity (-9.8 m/s^2), and h is the maximum height reached by the stone.

Rearranging the equation, we get:

h = (vi^2)/(2g)

Substituting the given values, we have:

h = (35 m/s)^2 / (2 * 9.8 m/s^2)

= 62.6 m

Therefore, the maximum height reached by the stone is approximately 63 m.

The answer is (d).

Answer: Pressure of gases.

Explanation:

In a heat engine, the air-fuel mixture is ignited, which causes an increase in pressure of the gases inside the cylinder. This pressure pushes the piston, which is connected to a crankshaft, causing it to rotate and do work. Therefore, pressure is an essential property of gases for the ability of a heat engine to do work.

Explanation:

INITIAL  Vertical velocity is given by

30 m/s * sin 37

 then gravity begins to slow it down

30 sin37  -  (9.81) t   = vertical velocity at  t

    when v = 0 , the car is at its apex and will fall back down in the same amount of time

  0 = 30 sin37 - 9.81 t      shows t = 1.84 seconds to peak

    then another 1.84 seconds to fall to the ground   total = 3.7 seconds

The tractive force of the engine is 1020 N.

Mass of the car, m = 750 kg

Acceleration of the car, a = 1.5 m/s²

Traction, also known as tractive force, is the force used to produce or create motion by using dry friction between a body and an inclined surface.

Weight of the car, W = mg

W = 750 x 9.8

W = 7350

The coefficient of friction is the ratio or percentage of the opposing frictional force to the normal force pressing the two surfaces into contact and motion.

The tractive force of the engine,

F' = ma - mg sinθ = m(a - g sinθ)

F' = 750[1.5 - (9.8/70)]

F' = 750 x 1.36

F' = 1020 N

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Answer:

Explanation:

To find the angle of deviation, we can use the formula:

angle of deviation = (refractive index of metal - refractive index of air) x angle of incidence

The angle of incidence can be calculated using Snell's law:

sin(angle of incidence) / sin(angle of refraction) = refractive index of air / refractive index of metal

sin(angle of incidence) / sin(25°) = 1 / 1.75

sin(angle of incidence) = 0.5714

angle of incidence = 34°

Now we can substitute this value into the formula for angle of deviation:

angle of deviation = (1.75 - 1) x 34°

angle of deviation = 21°

Therefore, the angle of deviation is 21°.

To correct the issue of flipped imagery caused by mirrors you can use a technique called "mirror flipping". Mirror flipping involves using a second mirror to reflect the reflected image from the first mirror which then flips it back to its original orientation

Alternatively you can use a prism to correct the orientation of the image. A prism is a transparent object that can bend light. By placing it infront of the mirror you can reflect the twice, effectively helping in the correction of the orientation of the image

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